Slope and Point-Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

How do you calculate slope using two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by the equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

Write the point-slope form of the line with slope 2 that passes through the point (3, 4).

Back

y - 4 = 2(x - 3).

Front

What is the significance of the point (x1, y1) in the point-slope form?

Back

The point (x1, y1) represents a specific point on the line, which is used to define the line's position.

Front

If a line has a slope of -4, what does this tell you about its direction?

Back

A slope of -4 indicates that the line falls steeply from left to right.